Question: Simplify the following expression: $ r = \dfrac{-4}{7} + \dfrac{t + 7}{t + 4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{t + 4}{t + 4}$ $ \dfrac{-4}{7} \times \dfrac{t + 4}{t + 4} = \dfrac{-4t - 16}{7t + 28} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{t + 7}{t + 4} \times \dfrac{7}{7} = \dfrac{7t + 49}{7t + 28} $ Therefore $ r = \dfrac{-4t - 16}{7t + 28} + \dfrac{7t + 49}{7t + 28} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-4t - 16 + 7t + 49}{7t + 28} $ $r = \dfrac{3t + 33}{7t + 28}$